Mathematics – Numerical Analysis
Scientific paper
2007-09-10
Mathematics
Numerical Analysis
18 pages, 6 figures; v2: example and figures added, minor correction to example 2; v3: added section on nonholonomic Stoermer-
Scientific paper
10.1088/0951-7715/21/8/009
In this paper, we propose a geometric integrator for nonholonomic mechanical systems. It can be applied to discrete Lagrangian systems specified through a discrete Lagrangian defined on QxQ, where Q is the configuration manifold, and a (generally nonintegrable) distribution in TQ. In the proposed method, a discretization of the constraints is not required. We show that the method preserves the discrete nonholonomic momentum map, and also that the nonholonomic constraints are preserved in average. We study in particular the case where Q has a Lie group structure and the discrete Lagrangian and/or nonholonomic constraints have various invariance properties, and show that the method is also energy-preserving in some important cases.
de Diego David Martin
Ferraro Simone
Iglesias David
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